In this context, the bootstrap is used to replace sequentially empirical weighted probability measures by empirical measures. Bootstrapping techniques are also used in the updating-selection transitions of particle filters, genetic type algorithms and related resample/reconfiguration Monte Carlo methods used in computational physics.

It is often used as a robust alternative to inference based on parametric assumptions when those assumptions are in doubt, or where parametric inference is impossible or requires very complicated formulas for the calculation of standard errors. It may also be used for constructing hypothesis tests. It has been called the plug-in principle, as it is the method of estimation of functionals of a population distribution by evaluating the same functionals at the empirical distribution based on a sample.įor example, when estimating the population mean, this method uses the sample mean to estimate the population median, it uses the sample median to estimate the population regression line, it uses the sample regression line. Main article: Bootstrap (statistics) The best example of the plug-in principle, the bootstrapping method.īootstrapping is a statistical method for estimating the sampling distribution of an estimator by sampling with replacement from the original sample, most often with the purpose of deriving robust estimates of standard errors and confidence intervals of a population parameter like a mean, median, proportion, odds ratio, correlation coefficient or regression coefficient.

Permutation